Overview of Magnetic Measurement Techniques

Overview ofMagnetic Measurement

TechniquesAnimesh Jain

Brookhaven National LaboratoryUpton, New York 11973-5000, USA

US Particle Accelerator School on Superconducting Accelerator MagnetsSanta Barbara, California, June 23-27, 2003

USPAS, Santa Barbara, June 23-27, 2003 Animesh Jain, BNL2

Outline• Nuclear Magnetic Resonance (NMR)/

Electron Paramagnetic Resonance (EPR)• Hall Probes• Magnetoresistors• Fluxgate Magnetometers• Flux Measurements with Pick Up Coils• Magnetic Alignment – center and direction• Summary


NMR/EPR Principle• A particle with a spin and a magnetic

moment precesses around an applied field.• The quantum energy levels are split into

several discrete levels, depending on thespin of the particle.

• The energy gap between these levels is proportional to the applied field.

• A resonant absorption of RF energy occurs at a frequency corresponding to energy gap.


NMR/EPR PrincipleI = Spinγ = Gyromagnetic ratio

M = Magnetic Moment= γ.h.I

Energy = B.MSpin component along the field direction can take integral values from –I to +I. ⇒ Energy gap = γ.h.B

Frequency = γ.B

B

M

MagneticMoment

AppliedField

Precession


Gyromagnetic Ratio

Particle γ (MHz/T) Application

e– 28026.5 0.5 to 3.2 mT1H 42.576396 0.04 to 2 T2H 6.53569 2 T to 14 T

3He 32.4336 Cryogenic27Al 11.0942 Cryogenic


NMR Magnetometer

ModulationOscillator

Sample&

Hold

Trigger

Probe

∆B/B ~ 10–4 to 10–3; 30-70 Hz

RF

B

∆B

VCO


Locking RF to NMR Resonance

B0

B0+∆B(t)

B0

B0+∆B(t)

NMR Signalwith

f and B0mismatched

NMR Signalwith

f and B0matched

Error

Resonance occurs at non-zero value of modulating signal.

NMR signals arrive at uneven intervals.

Resonance occurs at Zero value of modulating signal.

NMR signals arrive at even intervals.


Requirements for NMRNMR can provide measurement of magnetic field with absolute accuracy of 0.1 ppm. However, certain requirements must be met:

• Field must be stable (< 1% per second).• Field must be homogeneous (< 0.1% per cm):

– The signal deteriorates; difficult to lock– Probe positioning accuracy becomes critical.One may locally compensate for the gradient using small gradient coils, to make measurements in inhomogeneous fields.


The Hall Effect

–

––

–

–

BB⊥ I

F

VHall

v

+

θ

Charge carriers experience a Lorentz force in the presence of a magnetic field.

This produces a steady state voltage in a direction perpendicular to the current and field.

G = Geometric factor

RH = Hall Coefficient

θ⋅⋅⋅= cosHall BIRGV H


The Planar Hall Effect

B B||

I

VPlanar

+ψ

Curre

nt

If the field has a component in the plane defined by current flow and voltage contacts, then a signal is produced given by:

Important for mapping of 3-D fields.

)2sin(2||Planar ψ⋅∝ BIV

The Planar Hall Effect can be minimized by a suitable choice of geometry ⇒ sin(2ψ) = 0.In practice, the response of a Hall probe to the field direction is considerably more complex, requiring elaborate calibration.


Compensating Planar Hall Effect- 2 Matched Hall probes- I directions as shown- Major component = By

is in the plane of theHall probes.

Sum of Planar Hall Voltages is proportional to:

[ ][ ]12

21

90 ;0)2sin()2sin(

ψ+°=ψ=ψ+ψ

Based on:R. Prigl, IMMW-11, BNL.


Hall Measurement Specifications

• Typical Range: < 1 mT to 30 T

• Typical Accuracy ~ 0.01% to 0.1%

• Typical dimensions ~ mm

• Frequency response: DC to ~ 20 kHz(~ a few Hz for fully compensated signal)

• Time Stability: ±0.1% per year


Hall Measurement Advantages• Simple, inexpensive devices, commercially

available.• Small probe size makes it suitable for a

large variety of applications.• Can measure all components of field.• Particularly suited for complex geometries,

such as detector magnets.• Can be used for fast measurements.• Can be used at low temperatures.


Hall Measurement Disadvantages• Non-linear device, requires elaborate

calibration of sensitivity for each probe.• Sensitive to temperature: Calibrate as a

function of temperature; Keep temperature stable; Design compensated probes.

• Long term calibration drift.• Planar Hall effect can pose a problem for

mapping 3-D fields. Special geometries are needed for measuring minor components.


Magneto-ResistorsB

I

VNiSb Precipitates

InSb Slab

Field bends the current path, thus altering the resistance.Hall voltage tends to reduce this effect.

NiSb precipitates “arrest” the build-up of charge on the sides; Non-linear device; Insensitive to polarity; Large temperature dependence; Modest sensitivity.Based on: L. Bottura, Field Measurement Methods, CERN School on Superconductivity, Erice, May 8-17, 2002.


Fluxgate MagnetometersB

excitationcoil

bias coil

detection coil

+Bexcitation

-Bexcitation

B

excitationcoil

bias coil

detection coil

+Bexcitation

-Bexcitation

Courtesy: L. Bottura, CERN.

Excitation Coil:AC current drives a pair of ferromagnetic needles to saturation.Detection Coil:Detects Zero field condition.Bias Coil:Maintains a zero field condition.


Fluxgate Principle: Zero FieldM

H

t

H

M

t

M1

M1+M2

M2

V

t

Excitation Profile (H ) is symmetric

Based on: L. Bottura, CAS on Superconductivity, Erice, 2002

Zero output in detection coil


M

H

t

HH0

V

t

M

t

M1

M2

M1+M2

Excitation Profile (H ) is asymmetric Based on: L. Bottura, CAS on

Superconductivity, Erice, 2002

Output of detection coil

Fluxgate Principle: Non-Zero Field


Fluxgate Characteristics• Highly sensitive, linear, directional device.• Typical field range ~ a few mT.

(Limited by capability of the bias coils)• Bandwidth: DC to ~ 1 kHz.• Sensitivity: ~ 20 pT (~1 nT commercial).• Accuracy: ~ 0.1%

(depends on calibration and stability)• Used in navigation, geology, mapping of

fringe fields, etc.


excitationcoil

biascoil

detectioncoil

B

I

Current to be measured

Courtesy:L. Bottura, CERN.

DC Current Transformer

Senses magnetic field produced by a current carrying conductor passing through a toroidalcore.Used for accurate measurement of high currents(~10-100 ppm typical)

DCCT: A Special Fluxgate


Flux Measurements: Induction LawFlux through a coil defined by the surface S is:

B

SV(t)

Coil

∫ ⋅=ΦS

d SB

If the flux linked varies with time, a loop voltage is induced, given by:

⋅−=

Φ−= ∫

S

ddtd

dtdtV SB)(

The time dependence may be caused by either a varying field or a varying surface area vector, or both.


Flux MeasurementsTime dependence of flux gives:

B

SV(t)

Coil

⋅−=

Φ−= ∫

S

ddtd

dtdtV SB)(

The change in flux is given by:

⌡⌠ ⋅−=Φ−Φend

start

t

t

startend dttV )(

and can be measured by integrating the voltage signal.

To know the flux at a given instant, one needs to know Φstart

⇒ (1) Use Φstart = 0; (2) Flip Coil/Rotating coil: startend Φ=Φ m


ab

h

Point Coil Insensitive up to4th order spatial harmonic with proper choice of height and radii.

Rc

X

Y

θπ/m

θ'=θ+π/(2m)

Multipole Coil Sensitive to only odd multiples of a specified harmonic (Morgan Coils)

Flat Coil (Line or Area Coil) –Fixed coil; Varying field–Flip Coil/Moving Coil; Static field–Rotating Tangential/Radial

Common Coil Geometries


Flux Measurements: Hardware

± 5 VVin(t) G 0-10 V

Counters

N

NrefVref(+5 V)

Referencefrequencyfref = α fmax

VFC10 V = fmax

Digital Integrator: Directly gives change in flux.10-100 ppmaccuracy.

Digital Votmeter: Gives rate of changeof flux. Numerical Integration and/or well controlled coil movement is needed.


Measurements with Pick up Coils• Simple, passive, linear, drift-free devices.• Require change in flux ⇒ ramp field with

static coil, or move coil in a static field. Pay attention to ramping/moving details.

• Measure flux, not field. ⇒ Calibration of geometry very important; limits accuracy.

• Field variations across the coil area must be accounted for ⇒ harmonic analysis.

• Field harmonics can be measured at ppm level.• Field direction can be measured to ~ 50 µrad.


Determination of Magnetic Center

MAGNET

To Integrator

X-Y Stage Wire

Stretched Wire Measurements• Move a stretched wire in a magnet• Measure change in flux for various types of motion.

• Use expected field symmetry to locate the magnetic center.

Colloidal Cell• Place ferromagnetic fluid in the field

• Illuminate with polarized light

• Observe with crossed analyzer


Rotating Coils• Angular Encoder and Gravity Sensors

• Accuracy 50-100 µrad• Frequent re-calibrations

EncoderEncoder

Gravity Gravity SensorsSensors

CoilCoilDetermination of Field Direction

LASER

BEAMSPLITTER

MAGNETICNEEDLE

MIRROR

OPTICALFILTER

POSITION SENSITIVE DETECTOR

Mirror& Needle

• For solenoids• Resolution~ 10 µrad

Based on: C. Crawford et al., FNAL and BINP, Proc. PAC'99, p. 3321-3


Summary• Numerous methods exist for measurement of

magnetic fields. Only some of them are in common use for measuring accelerator magnets.

• NMR technique is the standard for absolute accuracy, but can not be used in all situations.

• Hall probes are very popular for point measurements, such as for field mapping of detector magnets.

• A variety of pick up coils are the most often used tools for characterizing field quality in accelerator magnets.

• Innovative techniques have been developed for alignment measurements to suit various applications.


For More Information• Knud Henrichsen’s bibliography:

http://mypage.bluewin.ch/hera/magnet

• CERN Accelerator Schools on Magnetic Measurements:– March 16-20, 1992, Montreux (CERN 92-05, 15 Sep. 1992)– April 11-17, 1997, Anacapri (CERN 98-05, 4 Aug. 1998)

• Proceedings of Magnet Measurement Workshops:– IMMW-1 (1977) to IMMW12 (2001); IMMW13 (May 2003)

• Proceedings of Particle Accelerator Conferences:– PAC (1965-2001); EPAC (1988-2002)

• Proceedings of Magnet Technology Conferences:– MT-1 (1965) to MT-17 (2001).

Documents

Overview of Magnetic Measurement Techniques